Cycles: Apply gradient to light cone setup with spotlight lamp
As mentioned in the comments under your question, this can be achieved using an emission shader connected to the volume output of a material with a gradient texture controlling the strength.

You will need to adjust the coordinates for the gradient texture however, as the default gradient texture has the gradient along the x axis. Using a texture coordinates node with the generated output connected to a mapping node we can position the texture however you like. To get the gradient in the direction you desire you will need to set the Y rotation to 90, which will rotate the gradient texture on the Y axis by 90 degrees, making it look like you want. You can also adjust the length over which the gradient falloff occurs by adjusting the z scale (lower values will stretch the texture more) and the X location (to move it up and down). The reason that you need to use X location instead of Z location is the mapping node applies location, then rotation, then scale, so the 90 degree rotation on the Y axis makes the X location become the Z location.

As josh sanfelici did in his setup, you can add a math node set to multiply (between the gradient texture and the emission shader) to control the strength, however in many cases you can get away with only positioning and scaling the texture to suit your needs.

Here is a node setup that will do what you want: